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Economics 304 Homework #3 – Dagwood and Homer and the Savings Function, Exams of Economic Analysis

Bay College Economic Analysis

A homework assignment for an Economics 304 course. It involves a two-period consumption model and the calculation of optimal consumption bundles for Dagwood, a borrower, and Homer, a lender. The document also requires the graphing of savings functions for Dagwood before and after changes in income, wealth, expected income, and expected wealth. step-by-step instructions and calculations for each question.

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Name __________________________ last 4 PSU ID _______

Please check section that you are registered in:

Section 001 - MWF: 9:05 - 9:55 AM : 112 Chambers Building __________

Section 002 - MWF: 11:15 AM - 12:05 PM : 22 BBH Building ____________

Fall 2018 Chuderewicz - YOU MUST HAND IN HW IN THE SECTION YOU ARE

REGISTERED FOR - NO EXCEPTIONS

YOU MUST USE THIS AS A TEMPLATE – THAT IS – MAKE SPACE FOR YOUR

ANSWERS BY HITTING ENTER (you certainly don’t need to type this assignment)–

LEAVE THE QUESTIONS AS THEY ARE – AND PLEASE STAPLE! NOTEBOOK PAPER

(OR ANY PAPER) STAPLED TO THE BACK IS NOT ACCEPTABLE (GETS A ZERO).

ALSO, PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME IN THE TOP

RIGHT HAND CORNER OF THIS PAGE SO THAT WE CAN ALPHABETIZE THESE

EASILY. THANKS IN ADVANCE!

Economics 304

Homework #3 – Dagwood and Homer and the Savings Function

Due Wednesday, 9/19 at the beginning of class – you must hand in homework in the section

you are registered in - no late papers accepted!

Instructions: Please show all work or points will be taken off. Good luck!

Suppose we have Dagwood, who has a current income of $150K and expected future income of

$100K. He has $ 20K in current wealth (i.e., ‘a’ = $20K), He has zero expected future wealth

(i.e., af = 0).

Dagwood’s behavior is consistent with the

life-cycle theory of consumption. For one,

he perfectly smoothes consumption and

two, since he is in his peak earning years,

he is saving now so that he can maintain

his current level of consumption in the

future. Given that Dagwood faces a real

interest rate of - 0.04, answer the

following questions.

a) (5 points) Calculate Dagwood’s

optimal consumption bundle showing all

work. Then draw a completely labeled

graph (the two period consumption

model) depicting this initial optimal

Partial preview of the text

Download Economics 304 Homework #3 – Dagwood and Homer and the Savings Function and more Exams Economic Analysis in PDF only on Docsity!

Name __________________________ last 4 PSU ID _______ Please check section that you are registered in: Section 001 - MWF: 9:05 - 9:55 AM : 112 Chambers Building __________ Section 002 - MWF: 11:15 AM - 12:05 PM : 22 BBH Building ____________ Fall 2018 Chuderewicz - YOU MUST HAND IN HW IN THE SECTION YOU ARE REGISTERED FOR - NO EXCEPTIONS YOU MUST USE THIS AS A TEMPLATE – THAT IS – MAKE SPACE FOR YOUR ANSWERS BY HITTING ENTER (you certainly don’t need to type this assignment)– LEAVE THE QUESTIONS AS THEY ARE – AND PLEASE STAPLE! NOTEBOOK PAPER (OR ANY PAPER) STAPLED TO THE BACK IS NOT ACCEPTABLE (GETS A ZERO). ALSO, PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME IN THE TOP RIGHT HAND CORNER OF THIS PAGE SO THAT WE CAN ALPHABETIZE THESE EASILY. THANKS IN ADVANCE! Economics 304 Homework #3 – Dagwood and Homer and the Savings Function Due Wednesday, 9/19 at the beginning of class – you must hand in homework in the section you are registered in - no late papers accepted! Instructions: Please show all work or points will be taken off. Good luck! Suppose we have Dagwood, who has a current income of $150K and expected future income of $100K. He has $ 20K in current wealth (i.e., ‘a’ = $20K), He has zero expected future wealth (i.e., af^ = 0). Dagwood’s behavior is consistent with the life-cycle theory of consumption. For one, he perfectly smoothes consumption and two, since he is in his peak earning years, he is saving now so that he can maintain his current level of consumption in the future. Given that Dagwood faces a real interest rate of - 0.04, answer the following questions. a) (5 points) Calculate Dagwood’s optimal consumption bundle showing all work. Then draw a completely labeled graph (the two period consumption model) depicting this initial optimal

consumption bundle as point CA (please use the space below). Note, for all C calculations, round down to one decimal point.

CA* = [(1 + (-0.04))(150 + 20) + 100 ] / (2 + (-0.04))

CA* =134.29, 134.

CB* = [(1 + (-0.04))(210 + 40) + 200 + 50 ] / (2 + (-0.04))

CB* = 250, 250

CC* = [(1 + (0.07))(250 + 50) + 200 + 100] / (2 + (0.07))

CC* = 250,

(15 points for a completely labeled graph – be sure to label the no lending / no borrowing points = NL/NB and the slope of each budget constraint)

CA* = [(1 + (-0.04))(200 ) + 200 ] / (3 + 2 x (-0.04))

CA* =268.5, 134.

CB* = [(1 + (-0.04))(100) + 100 ] / (3 + 2 x (-0.04))

CB* = 134.25, 67.

CC* = [(1 + (0.07))(100) + 100] / (3 + 2 x (0.07))

CC* = 131.85, 65.

(15 points for a completely labeled graph – be sure to label the no lending / no borrowing points = NL/NB and the slope of each budget constraint) b) (5 points) Homer goes to work and the rumor being spread around the work place is not good. Homer works in the ‘green energy’ field and given the new head of the EPA, green energy grants are being cut. Homer is forced to take a pay cut so that his current income (Y) falls to $100K and his future expected income also falls to 100K (a permanent shock to his income). Recalculate the optimal bundle for Homer and add this point to your graph and label as point C*B.

c) (5 points) In steps Jerome Powell and the Fed. Given that the economy appears to be on sound footing, the Fed raises interest rates so that the real rate of interest rises to 0.07. Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CC. (Note, point CC incorporates the shock to wealth in part b)) d) (10 points) Is Homer better or worse off due to the RISE in the real rate of interest? Explain being sure to discuss exactly how the substitution and income effects play a role in Homer's consumption decisions. Also, comment on whether these income and substitution effects work in the same or opposite direction (i.e., is it a tug of war or do they work in the same direction?) in this particular case. Please include actual numbers when discussing the income and substitution effects or points will be taken off. NO - worse off..... Since Homer is a borrower, he cares most about his PV of future resources since he is financing consumption today by borrowing from the future. When r goes up, PV = (yf^ + af) / (1 + r) falls and therefore Homer is poorer and should spread the pain and consume less in both periods - this is the income effect. With numbers: PV = 100 / (1 + (-.04)) = 104.17 vs PV = 100 / (1 + (.07)) = 93.46. The substitution effect works in the same direction - when r goes up so does the price of current consumption = 1+r / 1. The price of current consumption goes from .96 units of future consumption to 1.07 units of future consumption - since the price of current consumption has gone up, Homer should substitute away from current consumption towards future consumption. The income effect and substitution effect work in the SAME direction since both imply Homer should consume less in the current period!

S = Y = C

POINT A: 15.79 = 150 - 134.

POINT B: 13.82 = 150 - 136.

WORK FOR POINT B

CA* = [(1 + 0.07))(150 + 20) + 100 ] / (2 +.07))

CA* =136.18, 136.

POINT C: -40 = 210 - 250

POINT D: -40 = 210 - 250

i) What has happened to Dagwood’s savings rate?

THE SAVINGS RATE (S/Y) FELL....WAS 15.79 / 150 = 10. 53 % AND NOW IT IS -40/

b)(25 points total) We are going to graph two savings functions for Homer. The first savings function to draw refers to the savings initially, before Homer gets the bad news at work. Calculate the level of savings at the point CA^ and label as point A on your diagram. Now you need to do some work. Calculate the level of savings if Homer did not receive a change in his current income and expected income and Jerome Powell and the Fed raised interest rates to 0.07. Hint: you simply need to calculate what Homer's consumption would have been under these conditions and then calculate his savings.... label this as point B, connect points A and B and we have Homer's first savings function. The second savings function is after the change in Homer’s current and expected income. Label as point C, Homer's saving at point CB^ and then label as point D, Homer's saving at point CC*. Connect points C and D and we have the second savings function for Homer. Be sure to label your diagram completely including all the shift variables that we are holding constant along any savings function with the signs ( + or - ) above the shift variables. S = Y = C POINT A: -68.5 = 200 - 268. POINT B: -63.7 = 200 - 263. WORK FOR POINT B

CA* = [(1 + 0.07))(200) + 200 ] / (3 + (2 x .07))

CA* =263.7, 131.

POINT C: -34.5 = 100 - 134.

POINT D: -31.85 = 100 - 131.

i)( Did Homer's savings increase or decrease because of his change in current and expected income - explain using the definition of savings: S = Y - C. point distribution : 20 points for completely labeled graph along with showing all work to calculate savings for all points: A, B, C, and D and 5 points for answering i) above. Homer's saving function increased - current income falling would result in lower savings but the fall in expected income would raise savings - using S = Y - C